Transport Network analysis often requires to model transitions as order 1 markovian models. Previous works suggest the use of higher order models in order to build networks that can more accurately predict observed sequences. In this work, we compare these models' prediction capabilities and size using different real world trajectories datasets. Beside generic models, we introduce models that include exogenous variables such as the location or the categories of the visited places. They provide further research opportunities. Our experimental results suggest that the HON model (Xu et al. (2016)) offers a good compromise between predictive capabilities and parsimony. However, some claimed properties of this model could not be reproduced. Indeed, none of the strategies used here results in better predictions than the fix-order model (Rosvall et al. (2014)).